Noise in electrical circuits, which is mainly caused by the nature of the semiconductors used, is a hindrance to the incoming signals because it interferes in the demodulation of the signals in the back-end of a radio. It is important to suppress all noise sources at the beginning or the input of the receiver-chain so that the noise does not get amplified by the first circuit.
Since the noise is a natural phenomenon, it is not easy to minimize, except by filtering out the part of the incoming electro-magnetic spectrum that is not occupied by the signal, and by ensuring that maximum power transfer occurs between the antenna and the input of the front-end of a radio. Noise can be further minimized by filtering the output of the amplifier so that those frequencies not within the signal bandwidth are attenuated rather than amplified.
The first circuit to receive the incoming Radio Frequency (RF) signal from the antenna is a tuned amplifier, or a tuned Low Noise Amplifier (LNA). FIG. 1 illustrates an LNA circuit. An LNA is a circuit that amplifies an input signal within a specified Band-Width (BW), while contributing a Noise Figure (NF) small enough so that the Noise Power (Pn) at its output does not affect the rest of the circuit in the RF receiver chain. The LNA is biased in such a way as to minimize its own noise contribution which arises from its components.
Inductors are used to tune the output of the LNA. This kind of an inductor is used in an LC-tank and thus called a “tank-inductor”. Here the source of noise in the inductor is less of a concern, as the gain of the LNA causes the output signal to noise ratio to be high as long as the input noise is kept low by minimizing the thermal noise contributed by the resistive elements of the input matching network and the amplifier itself. This minimizes the effective NF, given by equation (1).
                    NF        =                              SNR                          i              ⁢                                                          ⁢              n                                            SNR            out                                              (        1        )            
However, the Q of the active inductors that are used to miniaturize the circuits are also low at higher frequencies, and thus the resulting Q of the LC-tank is low (Qs add in a similar manner as resistors in parallel for QC and QL). For a high gain, which is required to keep the NF in the system low, a high-Q output tank is required to provide a large output impedance to the amplifier.
Accordingly, for operation at higher frequencies, large inductors are required in tuned circuits, and at lower frequencies, large capacitors are required. Further, inductors have low performance at higher frequencies (about 3 GHz) and therefore it becomes economically inefficient to use inductors at those frequencies in integrated circuits (ICs).
The LNA should also have high gain (defined as the ratio of output small-signal Voltage or Power to the input small-signal Voltage or Power) because this renders the noise effect caused by the following circuit components to be negligible.
In addition to providing a low NF, the LNA suppresses the 2nd order harmonic distortions and 3rd order inter-modulation product frequencies not only in order to meet the specifications required for the design of the LNA, but also in order to provide a “clean” output signal to the rest of the components in the receiver chain.
The main purpose of the LC-tank is to store energy obtained from the current and voltage swings produced by the amplifying transistors. This energy cannot be stored perfectly because of the series and parallel resistances in the inductor and capacitor in the tank. Thus there is an effect of loss in the stored energy. However the storage results in a large voltage swing required for amplification. The LC-tank in this case also acts as a resonator in the sense that the inductor produces the voltage from the change in the current swing provided by the amplifying transistor. This voltage change in turn produces the current through the capacitor in the tank, which in turn adds to the initial current through the inductor which would be quite small. The extract current produces a further voltage drop across the inductor, which in turn increases the total amplification of the amplifier without adding resistive noise in the circuit.
The above technique of using the LC-tank is useful for circuits where the size of the chip is not a concern. However, as the RF circuits become faster and require better performances from the on-chip inductors, the inductors get larger in size for better performances because they have a lower series resistance and therefore a higher Q, and thus there is a need to reduce the size of the inductor, or to replace the LC-tank altogether.
It has been previously proposed to replace the inductor in the LC-tank with an artificial or active inductor. There have been several designs made using gyrators, and active inductors. This is usually done to replace the high-Q inductors which are large in size and difficult to implement on ICs. Reducing silicon chip area is one of the most cost-saving goals of IC design. Some of the main uses of inductors are in LC-tank circuits. Designing active inductors which work relatively better at frequencies up to 10 GHz have been proposed. However, even these active inductors break down at frequencies higher than 10 GHz because of the parasitic capacitances intrinsic to active devices like MOSFETs and BJTs, and they work at frequencies below 3 GHz. At lower frequencies, the capacitor in the LC-tank is usually too large to be put on an IC, so that it has to be put off-chip.